Find the number base n 312basefour +52 n -96base ten
Find x if 101x =17 base ten find x
Yes
on the first one, should there be an = sign in there somewhere?
In any case 3124 = 3*4^3 + 1*4 + 2 = 19010
101x = 17
x^2 + 1 = 17
x^2 - 16 = 0
x = 4
1014 = 4^2+1 = 17
17
To find the number base (n), we can use the given equation:
312basefour + 52n - 96base ten = 0
Let's break down the equation and solve for n step by step:
1. Convert 312 from base four to base ten:
- The digits in base four are 0, 1, 2, and 3.
- The rightmost digit is multiplied by 4^0, the second-rightmost by 4^1, and so on.
- 312basefour = (3 * 4^2) + (1 * 4^1) + (2 * 4^0) = 48 + 4 + 2 = 54base ten
2. Replace 312basefour with 54base ten in the equation:
54base ten + 52n - 96base ten = 0
3. Simplify the equation by combining the base ten terms:
(54 - 96) + 52n = 0
-42 + 52n = 0
4. Move the constant term to the other side of the equation:
52n = 42
5. Solve for n by dividing both sides of the equation by 52:
n = 42 / 52 = 0.8077 (rounded to four decimal places)
Therefore, the value of n that satisfies the equation is approximately 0.8077